From Wikitravel's great piece on Rome:
Rome has excellent shopping opportunites of all kinds - clothing and jewellery (it has been nominated as a top fashion capital) to art and antiques. You also get some big department stores, outlets and shopping centres, notably in the suburbs and outskirts.
Main shopping areas include Via del Corso, Via Condotti, and the surrounding streets. The finest designer stores are around Via Condotti, whilst Via del Corso has more affordable clothing, and Via Cola di Rienzo, and the surroundings of Via del Tritone, Campo de'Fiori, and Pantheon are the places to go for cheaper items. Upim is a good shop for cheap clothing of workable quality. Some brands (like Miss Sixty and Furla) are excellent, some are not as good - be sure to feel garments and try them on. There are also great quality shoes and leather bags at prices that compare well with the UK and US. But when shopping for clothes note that bigger sizes than a UK size 16/US 12 aren't always easy to find. Children's clothing can be expensive with basic vests (tank tops) costing as much as €21 in non-designer shops. If you really need to buy clothers for kids try the Oviesse chain. Summer sales in many stores begin around July 15th and Rome also has New Year sales.
As mentioned above, Via Condotti is Rome's top haute couture fashion street (equivalent of Fifth Avenue in New York City, Via Montenapoleone in Milan, or Bond Street in London). Here, you can find big brand names such as Gucci, Armani, Dior, Valentino and Hermès, and several other high-class shops. However, the streets around the Via Condotti, such as Via Frattina, Via del Babuino, Via Borgognona and the Piazza di Spagna also offer some excellent high fashion boutiques, including Roberto Cavalli, Dolce & Gabbana, Versace, Prada and Givenchy (and several others). So once in the city, the big boutique names aren't absent. In these luxurious streets, however, you needen't only do clothing shopping - there are some really good and funky jewellery (e.g. Bulgari, Cartier, Tiffany's & Co.), pen and accessory (i.e. Mont Blanc) and artsy stores peppered here and there in these streets.
If you want to spend a day in a large shopping mall, there's the Euroma2 with about 230 shops (mainly clothes and accessories) and restaurants, to be found near the EUR district. Take Metro B line from Termini to EUR Palasport station, cross the road and take the frequent free bus (ride takes 5-15 minutes) to the mall. In addition to many shops and food, the conditioned air and free toilets may be a welcome relief if you are in Rome during mid-summer. La Rinascente, Rome's first department store, having been opened in 1887, is also a good retail department store, selling fashion, design, houseware and beauty products. If you like Abercrombie & Fitch or Hollister, you have an Abercrombie & Fitch Italia store in the Via Collatina.
There are lots of fake plastic 'Louis Vuitton' bags being sold at the side of the road. Be aware, that buying of fake products is illegal in Italy. Fines up to €1000 have been reported. If you are happy to take the risk, make sure you haggle; unsuspecting tourists pay up to €60 for them.
If you want to buy souvenirs or gifts, a museum would be the worst choice since there are many stalls along the streets of touristic areas that offer reasonable prices. It is likely that the same item in the gift shop of any museum will cost much more.
Castel Romano, near Rome, along the Via Pontina highway. A very large Factory Outlet with more than 100 branded shops. A car is needed to reach the place but a 30% discount in a designer shop is surely worth the 20km trip.
Valmontone. A little further away from Rome than Castel Romano, you can find Valmontone outlet on the motorway towards Napoli just 50 Km far from Rome. Valmontone itself is a delightful little town - 30 mins by train.